If your panel is full, you'll likely want to have the service evaluated, to determine if it's still large enough to meet your needs. It's possible that you may want to upgrade to a larger service, which will likely require new service conductors and a new service panel. If this is the case, you'll simply have a larger panel installed.
If you don't have/want to upgrade the service, you could still have a larger panel installed. Just make sure the new panel is larger enough for any future expansion.
If you do want to install a second panel, you'll have to determine what size feeder you want to supply it. This will dictate the wire size, and the size of the breaker supplying the new panel. To figure out what size feeder you'll want, you have to decide which circuits you'll move over to the new panel.
Once you've got that worked out, you'll have to reroute all the selected circuits to the new panel location. This could require making junctions in the old panel, to extend the length of the circuit.
All in all, I'd say this is not a project for a novice DIYer. There are a lot of subtle details that will likely be overlooked by a non-professional (and maybe even some "professionals"). My advice, would be to get quotes from a few local licensed electricians. Make sure to get pricing for the options I described above, and then decide how to proceed.
DO NOT JUST HIRE THE CHEAPEST BID